Abstract: It is difficult for designers to determine proper initial parameters for the optimal design of hydraulic supports. Based on the thought of visualized optimization design, the Euler-Savary equation and the inflection circle generation technology were applied to designing an approximate straight-line linkage for a hydraulic support. Firstly, some conditions were determined such as the pivot points which link the base with the front and back rod, the position of the pivot between the caving shield and roof beam, and the motion direction of the caving shield. Then, a mathematical model was established with the direction angle of the back linkage and the position angle of the inflection circle as design parameters, and it can be solved for all possible mechanisms with at least the second-order osculating straight-line. Mechanism property graphs of interest were computed and graphical visualization of the property information was implemented. Feasible solution regions adhering to design constraints were visually represented, which can rapidly guide designers to find the optimal mechanism with the minimum deviation for a given mining height, or the one with the maximum height for a given deviation, and provides a group of preliminary values with inherent advantage for the optimization design of hydraulic supports.